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Controlled transitions between phyllotactic states of repulsive particles confined on the surface of a cylinder

Phyllotactic states are regular lattice-like structures on cylinders and are a botanical classification scheme. In this communication, we report a sequence of transitions between phyllotactic states for particles with a repulsive particle-particle interaction on a cylindrical geometry at zero temperature. We can infer the transition points as a function of density via Monte Carlo simulations, as well as the mathematical descriptions of the ground states. The lattices we generate are described as phyllotactic states that fit onto the cylindrical surface as a set of helical chains. Our analysis shows how all state energies lie on the same parabola which we exploit to find the transitions.